A Comparison of Some Theoretical Models of Parallel Computation

In this paper we briefly describe and compare a number of theoretical models for parallel computation; namely, Petri nets, computation graphs, and parallel program schemata. We discuss various problems and properties of parallel computation that can be studied within these formulations and indicate the ties between these properties and the more practical aspects of parallel computation. We show how marked graphs, a particular type of Petri net, are a restricted type of computation graph and indicate how some results of marked graphs can be obtained from known results of computation graphs. Also, for schemata we discuss the decidability versus undecidability of various properties and several techniques of schemata composition.